Teamviewer on Linux

All-In-One: TeamViewer full version

This recommended download can establish connections as well as wait for incoming connections - one convenient solution for everything.

Installation Notes 

RedHat, CentOS, Fedora
Download rpm v7.0.9360		Red Hat 5, CentOS 5
Download rpm v7.0.9360		Red Hat 6, CentOS 6, Fedora

SUSE Linux Enterprise, openSUSE
Download rpm v7.0.9360		SLED, openSuse | 32-Bit
Download rpm v7.0.9360		SLED, openSuse | 64-Bit

Ubuntu, Debian
Download deb v7.0.9360		Debian, Ubuntu | 32-Bit
Download deb v7.0.9360		Debian, Ubuntu | 64-Bit

Other systems (not officially supported)
Download tar.gz v7.0.9360

TeamViewer will run on many other recent Linux flavors.
Please read

Installation on unsupported systems